MATLAB/SIMULINK for Engineering Applications day 2:Introduction to simulink
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Transcript of MATLAB/SIMULINK for Engineering Applications day 2:Introduction to simulink
“MATLAB EXPLORATION”
(Place to visualize your thoughts)Presentation By
Mr. ReddyPrasad Reddivari, Assistant Professor
Department of Electrical and Electronics EngineeringSri Venkateshwara College of Engineering
Bengaluru, Karnataka-562157Tel: 9494747497
E-Mail: [email protected]: www.reddyprasad.yolasite.com
MATLAB/SIMULINK for Engineering applications
Introduction to Matlab
Introduction to MATLAB and Simulink
What can you gain from the course ?
Know basics of MATLAB/Simulink– know how to solve simple problems
Know what MATLAB/Simulink is
Know how to get started with MATLAB/Simulink
Be able to explore MATLAB/Simulink on Be able to explore MATLAB/Simulink on your own !your own !
Introduction to MATLAB and Simulink
Contents
Built in functions
Getting Started Vectors and Matrices
Introduction
SimulinkModeling examples
MATLAB
SIMULINK
M–files : script and functions
IntroductionMATLAB – MATrix LABoratory
Initially developed by a lecturer in 1970’s to help students learn linear algebra. It was later marketed and further developed under MathWorks Inc. (founded in
1984) – www.mathworks.com Matlab is a software package which can be used to perform analysis and solve
mathematical and engineering problems. It has excellent programming features and graphics capability – easy to learn and
flexible. Available in many operating systems – Windows, Macintosh, Unix, DOS It has several tooboxes to solve specific problems.
Outline: What is Matlab? Matlab Screen Variables, array, matrix, indexing Operators (Arithmetic, relational, logical ) Display Facilities Flow Control Using of M-File Writing User Defined Functions plotting
What is Matlab? Matlab is basically a high level language
which has many specialized toolboxes for making things easier for us
How high?
Assembly
High Level Languages such as
C, Pascal etc.
Matlab
What are we interested in? Matlab is too broad for our purposes in this
course. The features we are going to require is
Matlab
CommandLinem-files
functions
mat-files
Command execution like DOS command window
Series of Matlab
commands
InputOutput
capability
Data storage
/ loading
Matlab Screen Command Window
type commands
Current Directory View folders and m-files
Workspace View program variables Double click on a variable to see it in the Array Editor
Command History view past commands save a whole session using diary
Variables No need for types. i.e.,
All variables are created with double precision unless specified and they are matrices.
After these statements, the variables are 1x1 matrices with double precision
int a;double b;float c;
Example:>>x=5;>>x1=2;
Mathematical Operators Mathematical Operators:
Add: + Subtract: - Divide: ./ Multiply: .* Power: .^ (e.g. .^2 means squared)
You can use round brackets to specify the order in which operations will be performed
Note that preceding the symbol / or * or ^ by a ‘.’ means that the operator is applied between pairs of corresponding elements of vectors of matrices
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Logical Operators
You can use Logical Indexing to find data that conforms to some limitations
Logical Operators: Greater Than: > Less Than: < Greater Than or Equal To: >= Less Than or Equal To: <= Is Equal: == Not Equal To: ~=
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Boolean OperatorsBoolean Operators:
AND: & OR: | NOT: ~
Connects two logical expressions together
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Special functions
There are a number of special functions that provide useful constants pi = 3.14159265…. i or j = square root of -1 Inf = infinity NaN = not a number
Array, Matrix a vector x = [1 2 5 1]
x = 1 2 5 1
a matrix x = [1 2 3; 5 1 4; 3 2 -1]
x = 1 2 3 5 1 4 3 2 -1
transpose y = x’ y = 1
2 5
1
Long Array, Matrix t =1:10
t = 1 2 3 4 5 6 7 8 9 10 k =2:-0.5:-1
k = 2 1.5 1 0.5 0 -0.5 -1
B = [1:4; 5:8]
x = 1 2 3 4 5 6 7 8
Generating Vectors from functions zeros(M,N) MxN matrix of zeros
ones(M,N) MxN matrix of ones
rand(M,N) MxN matrix of uniformly distributed
random numbers on (0,1)
x = zeros(1,3)x =
0 0 0
x = ones(1,3)x =
1 1 1
x = rand(1,3)x = 0.9501 0.2311 0.6068
Matrix Index The matrix indices begin from 1 (not 0 (as in C)) The matrix indices must be positive integer
Given:
A(-2), A(0)
Error: ??? Subscript indices must either be real positive integers or logicals.
A(4,2)Error: ??? Index exceeds matrix dimensions.
Matrix ReferenceConsider a 4-by-3 matrix
How is it arranged in memory?
A(1,1)A(2,1)A(3,1)A(4,1)A(1,2)A(2,2)A(3,2)A(4,2)A(1,3)A(2,3)A(3,3)A(4,3)
1234
5678
9101112
For 2-d double array, to move through memory sequentially– the first index changes the fastest, and– the second index changes the slowest
conversion: ind2sub, sub2ind
1st element2nd element3rd
4th
5th
6th
7th
8th
9th
10th
11th
12th
full index
linear index
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Concatenation of Matrices x = [1 2], y = [4 5], z=[ 0 0]
A = [ x y]
1 2 4 5
B = [x ; y]
1 2 4 5
C = [x y ;z] Error:??? Error using ==> vertcat CAT arguments dimensions are not consistent.
Operators (arithmetic)+ addition- subtraction* multiplication/ division^ power‘ complex conjugate transpose
Matrices Operations
Given A and B:
Addition Subtraction Product Transpose
Operators (Element by Element)
.* element-by-element multiplication
./ element-by-element division
.^ element-by-element power
The use of “.” – “Element” Operation
K= x^2Erorr: ??? Error using ==> mpower Matrix must be square.B=x*yErorr:??? Error using ==> mtimes Inner matrix dimensions must agree.
A = [1 2 3; 5 1 4; 3 2 1] A = 1 2 3 5 1 4 3 2 -1
y = A(3 ,:)
y= 3 4 -1
b = x .* y
b= 3 8 -3
c = x . / y
c= 0.33 0.5 -3
d = x .^2
d= 1 4 9
x = A(1,:)
x= 1 2 3
Basic Task: Plot the function sin(x) between 0≤x≤4π
Create an x-array of 100 samples between 0 and 4π.
Calculate sin(.) of the x-array
Plot the y-array
>>x=linspace(0,4*pi,100);
>>y=sin(x);
>>plot(y)0 10 20 30 40 50 60 70 80 90 100
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Plot the function e-x/3sin(x) between 0≤x≤4π Create an x-array of 100 samples between 0
and 4π.
Calculate sin(.) of the x-array
Calculate e-x/3 of the x-array
Multiply the arrays y and y1
>>x=linspace(0,4*pi,100);
>>y=sin(x);
>>y1=exp(-x/3);
>>y2=y*y1;
Plot the function e-x/3sin(x) between 0≤x≤4π Multiply the arrays y and y1 correctly
Plot the y2-array
>>y2=y.*y1;
>>plot(y2)
0 10 20 30 40 50 60 70 80 90 100-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Display Facilities plot(.)
stem(.)
Example:>>x=linspace(0,4*pi,100);>>y=sin(x);>>plot(y)>>plot(x,y)
Example:>>stem(y)>>stem(x,y)
0 10 20 30 40 50 60 70 80 90 100-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 10 20 30 40 50 60 70 80 90 100-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Display Facilities
title(.)
xlabel(.)
ylabel(.)
>>title(‘This is the sinus function’)
>>xlabel(‘x (secs)’)
>>ylabel(‘sin(x)’)0 10 20 30 40 50 60 70 80 90 100
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1This is the sinus function
x (secs)
sin(
x)
Operators (relational, logical)
== Equal to ~= Not equal to < Strictly smaller > Strictly greater <= Smaller than or equal to >= Greater than equal to & And operator | Or operator
Flow Control
if for while break ….
Control Structures If Statement Syntax
if (Condition_1)Matlab Commands
elseif (Condition_2)Matlab Commands
elseif (Condition_3)Matlab Commands
elseMatlab Commands
end
Some Dummy Examples
if ((a>3) & (b==5)) Some Matlab Commands;end
if (a<3) Some Matlab Commands;elseif (b~=5) Some Matlab Commands;end
if (a<3) Some Matlab Commands;else Some Matlab Commands;end
Control Structures
For loop syntax
for i=Index_ArrayMatlab Commands
end
Some Dummy Examplesfor i=1:100 Some Matlab Commands;end
for j=1:3:200 Some Matlab Commands;end
for m=13:-0.2:-21 Some Matlab Commands;end
for k=[0.1 0.3 -13 12 7 -9.3] Some Matlab Commands;end
Control Structures
While Loop Syntax
while (condition)Matlab Commands
end
Dummy Example
while ((a>3) & (b==5)) Some Matlab Commands;end
Use of M-FileClick to create a new M-File
• Extension “.m” • A text file containing script or function or program to run
Use of M-File
If you include “;” at the end of each statement,result will not be shown immediately
Save file as Denem430.m
Solution : use M-files
M-files : Script and function files
When problems become complicated and require re–evaluation, entering command at MATLAB prompt is not practical
Collections of commands
Executed in sequence when called
Saved with extension “.m”
Script FunctionUser defined commands
Normally has input & output
Saved with extension “.m”
Function is a ‘black box’ that communicates with workspace through input and output variables.
INPUT OUTPUTFUNCTION– Commands
– Functions
– Intermediate variables
M-files : script and function files (function)
Every function must begin with a header:
M-files : script and function files (function)
function output=function_name(inputs)
Output variableMust match the file name
input variable
Writing User Defined Functions
Functions are m-files which can be executed by specifying some inputs and supply some desired outputs.
The code telling the Matlab that an m-file is actually a function is
You should write this command at the beginning of the m-file and you should save the m-file with a file name same as the function name
function out1=functionname(in1)function out1=functionname(in1,in2,in3)function [out1,out2]=functionname(in1,in2)
Writing User Defined Functions
Examples Write a function : out=squarer (A, ind)
Which takes the square of the input matrix if the input indicator is equal to 1
And takes the element by element square of the input matrix if the input indicator is equal to 2
Same Name
Writing User Defined Functions Another function which takes an input array and returns the sum and product
of its elements as outputs
The function sumprod(.) can be called from command window or an m-file as
Notes: “%” is the neglect sign for Matlab (equaivalent
of “//” in C). Anything after it on the same line is neglected by Matlab compiler.
Sometimes slowing down the execution is done deliberately for observation purposes. You can use the command “pause” for this purpose
pause %wait until any keypause(3) %wait 3 seconds
Useful Commands
The two commands used most by Matlabusers are
>>help functionname
>>lookfor keyword
Plotting
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Plotting The plot function can be used in different ways:
>> plot(data)>> plot(x, y)>> plot(data, ‘r.-’)
In the last example the line style is definedColour: r, b, g, c, k, y etc.Point style: . + * x o > etc.Line style: - -- : .-
Type ‘help plot’ for a full list of the options
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Plotting A basic plot
>> x = [0:0.1:2*pi]>> y = sin(x)>> plot(x, y, ‘r.-’)
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0 1 2 3 4 5 6 7-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Plotting Plotting a matrix
MATLAB will treat each column as a different set of data
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1 2 3 4 5 6 7 8 9 100.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Plotting Some other functions that are helpful to create plots:
hold on and hold off title legend axis xlabel ylabel
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Plotting>> x = [0:0.1:2*pi];>> y = sin(x);
>> plot(x, y, 'b*-')
>> hold on
>> plot(x, y*2, ‘r.-')
>> title('Sin Plots');
>> legend('sin(x)', '2*sin(x)');
>> axis([0 6.2 -2 2])
>> xlabel(‘x’);
>> ylabel(‘y’);
>> hold off
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0 1 2 3 4 5 6-2
-1.5
-1
-0.5
0
0.5
1
1.5
2Sin Plots
x
y
sin(x)2*sin(x)
Plotting Plotting data
>> results = rand(10, 3)>> plot(results, 'b*')>> hold on>> plot(mean(results, 2), ‘r.-’)
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Plotting
Error bar plot>> errorbar(mean(data, 2), std(data, [], 2))
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0 2 4 6 8 10 120.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Mean test results with error bars
Plotting You can close all the current plots using ‘close all’
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Questions
? ? ? ? ?
Thank You…